On Unitary down-closed regular monomorphisms of pomonoid actions

Abstract

In this paper we characterize injective objects in the category of S-posets and S-poset maps for a pomonoid S, with respect to the class of unitary down- closed embeddings. Also, the behaviour of this notion of injectivity with respect to products and coproducts is studied. Then we introduce the notion of weakly regular d-injectivity in arbitrary slices of the category of S-posets, which is applied to investigate the Baer criterion. Finally we present an example to show that these objects are not regular injective, in general.

Mathematics Subject Classication (2010): 06F05, 18A32, 18G05, 20M30, 20M50.

Key words: S-poset, unitary down-closed embedding, weakly regular d-injective.